Fault-Tolerant Implementation of the Deutsch-Jozsa Algorithm

TL;DR

This paper demonstrates a fault-tolerant implementation of the Deutsch-Jozsa quantum algorithm using a minimal error-detecting code on a trapped-ion quantum computer, achieving significant noise reduction.

Contribution

It introduces a fault-tolerant method for the Deutsch-Jozsa algorithm using the smallest quantum error-detecting code without ancillae, and compares it to non-fault-tolerant execution.

Findings

Fault-tolerant implementation reduces noise in all oracles.

Average error rate reduction of nearly 90%.

Confidence level of approximately 99%.

Abstract

We show that one can implement the Deutsch-Josza algorithm, one of the first and simplest quantum algorithms, in a fault-tolerant manner using the smallest quantum error-detecting code -- the $[[4,2,2]]$ code -- without any ancillae. We implemented the algorithm on a trapped-ion quantum computer with and without fault-tolerant encoding and compared the results. With approximately $99 \%$ confidence, we found that the fault-tolerant implementation provided a noise reduction for all oracles. Averaged across all oracles, the reduction in error rate was nearly $90 \%$.